You know, it would probably be easier for everyone if you just asked your questions directly, instead of using the terminology improperly, and glazing things over like you know what you are talking about. You can look up what they mean yourself or... just ask. Nobody is going to make fun of you if you don't know what Codec or Aspect Ratio mean, especially if you show willingness to learn.

Codec has nothing to do with widescreen. Codec typically refers to the format your file is in. Almost like the language your computer uses to Code/Decode your footage, or rather what it uses to Read/Write the file. Examples are x264, XviD, and UTVideo.This should not be confused with Container, which refers to the method of encapsulating your Audio/Video Codecs. Examples of containers would be .mp4 .avi .mp3 .mkv (you can usually find this at the end of your file like "awesomeamv.mp4" If you don't see that dot followed by three characters, make sure you figure out how to show File Extensions on your computer first. By default, Windows hides those file extensions.)

AR (Aspect Ratio) typically refers to the ratio of width to height of a video during playback. The three AR's you will encounter the most are Fullscreen, Widescreen, and Extra-Widescreen (Scope). Numerically, those ratios would be 4:3, 16:9, and ~2.35:1 respectively. Examples of widths x heights that match these AR's would be 640x480, 1280x720, and 1280x544, if you just do the math/division.

An important note about AR: some footage, particularly DVD's, stretch during playback to match one of the above AR's. In North America, this usually means footage starts out as 720x480 (which has a 'wrong' AR of 3:2), and it stretches to 720x540 for Fullscreen, or ~854x480 for Widescreen. Which means, if you don't stretch your footage, it will be wrong. As such, this is a very common mistake for beginners and seasoned AMVers alike.

So then, how do you stretch your footage? Well, the easy way is to look for "Aspect Ratio" settings somewhere in your editing program. Do note, however, that some editing programs differentiate between three separate aspect ratios: the AR of your footage, the AR of your project, and in some cases, the AR of your final exported file too. If they all match, things usually work out the way you want, but sometimes it takes some experimentation to figure out what the program actually means when they say Aspect Ratio (sometimes AR can refer to the Pixel Aspect Ratio, PAR, which is the ratio of the Pixel's width to height, typically 1:1)

For me, I usually encode an entirely separate file resized to the correct AR so that I get exactly what I want, and I don't have to worry about AR issues, (among some other advantages like frame-accuracy and faster seek-times). The whole process can be a lot of work if you are not familiar, but that's what the guides are for: